Torque and Rotational Motion: every key term you need (+ practice quiz)
24 flashcard terms for AP Physics 1 Unit 7, written to match the course framework. Study them here, then drill them as interactive flashcards, or test yourself with the 24-question quiz — free, no account needed.
τ = r × F = rF sin(θ). Rotational analog of force. Causes angular acceleration. Units: N·m.
Moment of Inertia
I = Σmr²; rotational mass. Resistance to rotational acceleration. Higher I = harder to spin. Depends on mass distribution.
Rotational Second Law
τ_net = Iα. Torque = moment of inertia × angular acceleration. Analogous to F = ma.
Angular Acceleration (α)
Rate of change of angular velocity. α = Δω/Δt. Rad/s². Caused by net torque.
Rotational Kinetic Energy
KE_rot = ½Iω². Rotating object has energy depending on moment of inertia and angular velocity.
Angular Momentum
L = Iω. Conservation: if τ_net = 0, then L constant. Figure skater: pull arms in → ω increases.
Lever Arm
Perpendicular distance from pivot to force line. Longer lever arm → more torque. Same force, different arm = different torque.
Rolling Motion
v_cm = ωr. Combines translation + rotation. KE_total = ½mv_cm² + ½Iω². Energy split between translation/rotation.
Equilibrium Rotational
Στ = 0 (no rotation) and ΣF = 0 (no translation). Rigid body balanced.
Unit 7 Summary
Torque causes angular acceleration (τ = Iα). Angular momentum conserved if no external torque. Rolling combines linear + rotational motion.
Torque as r F sinθ
Only the force component perpendicular to the lever arm produces torque. Equivalently, torque = force × perpendicular distance from the pivot to the line of action.
Rotational Kinematics
With constant α: ω = ω₀ + αt, θ = ω₀t + ½αt², ω² = ω₀² + 2αθ. Every linear equation has a rotational twin; use radians throughout.
Linking Linear and Angular
v = rω, a_tangential = rα, a_centripetal = rω². Points farther from the axis move faster but share the same ω and α.
Moment of Inertia Shapes
Hoop: MR²; solid disk/cylinder: ½MR²; solid sphere: 2/5 MR²; hollow sphere: 2/3 MR²; rod about center: 1/12 ML²; rod about end: 1/3 ML². Mass far from the axis raises I.
Rolling Race
On an incline, objects with smaller I/(MR²) reach the bottom first: solid sphere beats solid cylinder beats hoop, independent of mass and radius.
Rolling Acceleration
For rolling without slipping down an incline, a = g sinθ / (1 + I/(MR²)); static friction supplies the torque and does no work.
Rolling Kinetic Energy
KE_total = ½Mv² + ½Iω² = ½Mv²(1 + I/(MR²)). A rolling hoop has half its energy in rotation; a solid sphere has 2/7 of it in rotation.
Static Equilibrium Two Conditions
ΣF = 0 AND Στ = 0 about any axis. Choose the pivot at the point where an unknown force acts to eliminate it from the torque equation.
L = mvr sinθ, so a particle moving in a straight line can have angular momentum about a point off its line of motion. This is what lets a moving putty stick change a rod's spin.
Angular Momentum Conservation Cases
Skater pulling in arms: I decreases, ω increases, KE increases (muscles do work). Two disks coupling: L conserved, KE lost to friction. Both are zero-external-torque cases.
Torque as Rate of Change of L
τ_net = ΔL/Δt, the rotational Newton's second law. Angular momentum changes only when a net external torque acts.
Massive Pulley
With a pulley of moment of inertia I, string tensions differ on the two sides; the difference times R equals Iα. Treat the pulley as an object with its own equation.
Rotational Work and Power
W = τΔθ, P = τω. A motor delivering constant power produces less torque at higher rotational speed.
Sign Conventions and Direction of ω
Counterclockwise is conventionally positive. Angular acceleration opposite to angular velocity means the rotation is slowing, just as in linear motion.